The present invention relates to a process for preparing acylsuccinic acid polyesters by reactingA) a polyester, which is the reaction product oi) maleic acid, maleic acid esters, maleic anhydride, fumaric acid and/or fumaric acid esters and optionally other diacids, monoacids or their derivatives withii) diols and optionally monofunctional alcohols,wherein the molar ratio of diols to diacids and their derivatives is 0.667:1 to 1.5:1, and the molar ratio of maleic acid and its derivatives+ fumaric acid and its derivatives to other diacids and their derivatives is greater than 0.15:1, and the molar ratio of monofunctional compounds to difunctional compounds is less than 0.4:1, withB) aliphatic C.sub.2 -C.sub.22 aldehydes and/or cycloaliphatic C.sub.6 -C.sub.20 aldehydes,in the presence of 0.2 to 10 % by weight (based on the weight of polyester) of free radical initiators at a temperature of 60 to 160.degree. C. and a pressure of 1 to 20 bar wherein the molar ratio of aldehydes to maleic acid ester and fumaric acid ester units is 1:1 to 50:1, and distilling off excess aldehyde.The present invention also relates to the acylsuccinic acid polyesters prepared by this process and to their use for the production of thermosetting plastics by reaction with di- or polyisocyanates such that 0.5 to 2 equivalents of isocyanate groups are used for each equivalent of acylsuccinic acid ester units.